The Multi-Depot Capacitated Arc Routing Problem (MDCARP) is an important combinatorial optimization problem with wide applications in logistics. Large Scale MDCARP (LSMDCARP) often occurs in the real world, as the problem size (e.g., number of edges/tasks) is usually very large in practice. It is challenging to solve LSMDCARP due to the large search space and complex interactions among the depots and the tasks. Divide-and-conquer strategies have shown success in solving large-scale problems by decomposing the problem into smaller sub-problems to be solved separately. However, it is challenging to find accurate decomposition for LSMDCARP. To address this issue and alleviate the negative effect of inaccurate problem decomposition, this article proposes a new divide-and-conquer strategy for solving LSMDCARP, which introduces a new restricted global optimization stage within the typical dynamic decomposition procedure. Based on the new divide-and-conquer strategy, this article develops a problem-specific Task Moving among Sub-problems (TMaS) process for the global optimization stage and incorporates it into the state-of-the-art RoCaSH algorithm for LSMDCARP. The resultant algorithm, namely, RoCaSH2, was compared with the state-of-the-art algorithms on a wide range of LSMDCARP instances, and the results showed that RoCaSH2 can achieve significantly better results than the state-of-the-art algorithms within a much shorter time.

中文翻译：

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RoCaSH2：针对大规模多站点容量弧路由问题的有效路由聚类和搜索启发式


多仓库电容弧路由问题（MDCARP）是一个重要的组合优化问题，在物流领域有着广泛的应用。大规模 MDCARP (LSMDCARP) 经常发生在现实世界中，因为问题规模（例如，边/任务的数量）在实践中通常非常大。由于搜索空间大以及仓库和任务之间复杂的交互，解决 LSMDCARP 具有挑战性。分而治之策略通过将问题分解为单独解决的较小子问题，在解决大规模问题方面取得了成功。然而，找到 LSMDCARP 的准确分解具有挑战性。为了解决这个问题并减轻问题分解不准确的负面影响，本文提出了一种新的分治策略来求解 LSMDCARP，该策略在典型的动态分解过程中引入了新的受限全局优化阶段。基于新的分而治之策略，本文为全局优化阶段开发了一种针对特定问题的子问题间任务移动（TMaS）流程，并将其纳入最先进的 LSMDCARP RoCaSH 算法中。所得到的算法，即 RoCaSH2，在各种 LSMDCARP 实例上与最先进的算法进行了比较，结果表明，RoCaSH2 可以取得比在 LSMDCARP 实例上最先进的算法明显更好的结果。时间要短得多。